Pith Number

pith:3I4M7PTR

pith:2021:3I4M7PTRZ5IKROQFYI6KDPT26M

not attested not anchored not stored refs pending

Bernoulli property of subadditive equilibrium states

Benjamin Call, Kiho Park

arxiv:2109.10721 v2 · 2021-09-22 · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3I4M7PTRZ5IKROQFYI6KDPT26M}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T06:54:59.168880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da38cfbe71cf50a8ba05c23ca1be7af3292bd1fff08b63db24015f9b0d60fc37

Aliases

arxiv: 2109.10721 · arxiv_version: 2109.10721v2 · doi: 10.48550/arxiv.2109.10721 · pith_short_12: 3I4M7PTRZ5IK · pith_short_16: 3I4M7PTRZ5IKROQF · pith_short_8: 3I4M7PTR

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3I4M7PTRZ5IKROQFYI6KDPT26M \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: da38cfbe71cf50a8ba05c23ca1be7af3292bd1fff08b63db24015f9b0d60fc37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e3293e7ad90711803fa78b0ef4012ccc07d675bbf2e42ca96dd758aba12e9d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2021-09-22T13:27:45Z",
    "title_canon_sha256": "7ac2acba6c08ebd7e8301f653bb0338179a7c6e84bb242c5bdc42c102969e217"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.10721",
    "kind": "arxiv",
    "version": 2
  }
}